The discovery of the atom in the early 19th century was an incredible scientific achievement and the mathematical developments of the time yielded indispensable modern techniques essential for understanding the behavior of noisy and random processes. These techniques have produced fundamental results in a wide range of fields, such as climatology, astronomy, economics, and many more. Today, in the field of active noisy systems — e.g., the study of objects that propel themselves but are subjected to noise (randomness), such as cells or autonomous robots — there is potentially another important juncture, where both the scientific and mathematical implications can innumerably benefit modern life. This project aims to discover and develop the fundamental mathematical framework for understanding these noisy active systems by developing accurate models of the individual agents, i.e., of a cell or single robot, and testing the models with experimental measurements. Movement of the individuals is a fundamental building block that’s vital to explicating the group or flocking behaviors present in, for example, living organisms, robotic explorations, or dynamically-adapting engineered materials. Scientifically, this project will advance our fundamental understanding of active noise and set the stage for developing applications in science and engineering. This research will take place in an interdisciplinary environment and students will be trained in the emerging scientific field of active noise.
Active noise exists in a wide range of systems, where it is often manifested as a non-equilibrium force that consistently induces complex dynamics. Recently, interest in active noise has grown rapidly because of its fundamental importance in the interdisciplinary fields of active matter and stochastic thermodynamics. This project will develop a mathematical framework to model active noise in self-propelled particles and its connection to physical law. Active self-propelled particles that consume energy to drive persistent motion are a model building block of many complex dynamical systems. Investigating how active noise drives dynamics holds promise to revolutionize our understanding of non-equilibrium systems and the associated mathematical techniques, much like our mathematical understanding of thermal noise revolutionized thermodynamics and material science. More specifically, self-propelled particles are by definition out-of-equilibrium and thus experience non-thermal active fluctuations. They serve as an ideal model system to study the non-equilibrium fluctuations of particles. This project will develop the mathematical framework for underdamped self-propelled particles. It will establish the foundational steps for understanding active noise by: (1) Building a stochastic model of self-propelled particles with the full inertial dynamics; (2) Developing a true model of active noise that mimics physical systems; and (3) Connecting active noise to relations in physics via stochastic thermodynamics. The generalized Langevin approach will be used for modeling, and experiments will done on both micro- and macro-scale self-propelled particles in confining potentials. Active noise is present in a wide variety of systems, including information systems, stochastic synchronization, fluid turbulence, active matter, living organisms, etc. Thus, studying how active noise can reveal the underlying dynamics of a system has potential to impact many fields.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
